Cette thèse porte sur l’étude des interactions entre les globules rouges (GRs)et l’endothélium, la couche des cellules qui délimite les vaisseaux sanguins.Il a été démontré que l’endothélium et les GRs jouent des rôles actifs dans divers processus du système vasculaire, et leurs interactions produisent un signal bio chimique grâce à des moyens à la fois chimiques (molécules de signalisation) et mécaniques (taux de cisaillement sur les parois). D’abord,nous étudions le rôle des GRs, y compris dans des conditions pathologiques, dans la création de contraintes de cisaillement spatialement et temporellement dynamiques sur l’endothélium. Il a été montré que les contraintes de cisaillement constituaient un élément critique dans le déclenchement d’un signal bio mécanique depuis l’endothélium. Par ailleurs, étant donné qu’il a été montré que les parois des vaisseaux sanguins ondulent en raison des cellules endothéliales individuelles qui le composent, nous avons intégré à notre modélisation cette géométrie. On trouve que cette ondulation affecte la dynamique des GRs dans l’écoulement ainsi que le taux de cisaillement sur les parois. Nous étudions rapidement dans quelle mesure la déformabilité d’un GR affecte sa trajectoire dans un vaisseau ondulé. Pour cela, nous nous inspirons du processus de fonctionnement un appareil de déplacement latéral déterministe (DLD) qui utilise les variations de trajectoires des particules en fonction de leur taille pour les séparer dans l’écoulement. Nous étudions par ailleurs l’effet des suspensions de GRs sur les caractéristiques rhéologiques et les contraintes de cisaillement sur la paroi du vaisseau.Finalement, nous nous adressons à les interaction chimiques en développons un modèle numérique avec la méthode de Boltzmann sur réseaux-limite immergée (LB-IBM) pour résoudre la diffusion et l’advectiond’un soluté libéré par un particule en mouvement et déformable. L’oxygène et l’adénosine triphosphate (ATP) sont toutes les deux libérées par les GRs,se diffusent dans l'écoulement, et sont absorbées par l’endothélium. Ils représentent des facteurs de signalisation critiques pour les processus de l’inflammation et vasodilatation. Nous montrons que la morphologie des GRs affectera le temps de résidence et la dilution des espèces chimiques lorsqu’elles rentreront en contact avec la paroi du vaisseau. Ensemble, ces éléments nous conduisent vers la développement d’un modèle capable de simuler des processus vitaux du système vasculaire qui résultent d’événements locaux de composants individuels. / This thesis is devoted to the study of the interactions between red blood cells (RBCs) and the endothelium, the monolayer of cells lining blood vessels. The endothelium and RBCs have been shown to be active participants in various processes in the vascular system, and their interactions trigger biochemical signalling by mechanical (wall shear stress) and chemical (signalling molecules) means. We first investigate the role of RBCs, including pathological conditions, in creating time- and space-varying shear stress on the endothelium. Shear stress has been shown to be a critical element in biochemical signalling from the endothelium. In addition, as it has been shown that the endothelium is undulating due to the individual endothelial cells comprising it, we take this into account in our model of the geometry of the vessel wall. We find that this undulation affects the dynamics of the RBCs in the flow and the wall shear stress. We briefly explore how the deformability of a single RBC affects its trajectory in undulating channels, inspired by the idea behind deterministic lateral displacement devices (DLDs) which exploit the differing trajectories of particles based upon their sizes to separate them in flow. We also investigate the effect of suspensions of RBCs in undulating channels on rheological properties and wall shear stress. Finally, we address the chemical interactions by building a numerical model with the lattice Boltzmann-immersed boundary method (LB-IBM) to solve advection-diffusion of solute released from moving, deformable particles. Oxygen and adenosine triphosphate (ATP) are both released by RBCs and are advected and diffused in the flow and uptaken by the endothelium and serve as critical signalling factors in inflammation and vasodilation. We find that the morphology of RBCs will affect the residence time and dilution of the chemical species upon contact with the wall. Together, these elements lead us towards the development of a model capable of simulating vital processes in the vascular system which result from local interactions of individual components.

No description available.

Centrosomin (Cnn) is an integral centrosomal protein in Drosophila with orthologues in several species, including humans. The human orthologue of Cnn is required for brain development with Cnn hypothesised to play a similar role in Drosophila. Control of Cnn incorporation into centrosomes is crucial for controlling asymmetric division in certain types of Drosophila stem cells. FRAP experiments on Cnn show that Cnn recovers in a pe- culiar fashion, which suggest that Cnn may be incorporated closest to the centrioles and then spread radially outward, either diffusively or ad- vectively. The aim of this thesis is to understand the mechanism of Cnn incorporation into the Drosophila centrosomes, to determine the mode of transport of the incorporated Cnn, and to obtain parameter estimates for transport and biochemical reactions. A crucial unknown in the modelling process is the distribution of Cnn receptors. We begin by constructing coupled partial differential equation models with either diffusion or advection as the mechanism for incorpo- rated Cnn transport. The simplest receptor distribution we begin with involves a spherical, infinitesimally thick, impermeable shell. We refine the diffusion models using the insights gained from comparing the model out- put with data (gathered during mitosis) and through careful assessment of the behaviour of the data. We show that a Gaussian receptor distribution is necessary to explain the Cnn FRAP data and that the data cannot be explained by other simpler receptor distributions. We predict the exact form of the receptor distribution through data fitting and present pre- liminary experimental results from our collaborators that suggest that a protein called DSpd2 may show a matching distribution. Not only does this provide strong experimental support for a key prediction from our model, but it also suggests that DSpd2 acts as a Cnn receptor. We also show using the mitosis FRAP data that Cnn does not exhibit appreciable radial movement during mitosis, which precludes the use of these data to distinguish between diffusive and advective transport of Cnn. We use long time Cnn FRAP data gathered during S-phase for this purpose. We fit the S-phase FRAP data using the DSpd2 profiles gath- ered for time points corresponding to the Cnn FRAP experiments. We also use data from FRAP experiments where colchicine is injected into the embryos to destroy microtubules (since microtubules are suspected to play a role in advective transport of Cnn). From the analysis of all these data we show that Cnn is transported in part by advection and in part by diffusion. Thus, we are able to provide the first mechanistic description of the Cnn incorporation process. Further, we estimate parameters from the model fitting and predict how some of the parameters may be altered as nuclei progress from S-phase to mitosis. We also generate testable predic- tions regarding the control of the Cnn incorporation process. We believe that this work will be useful to understand the role of Cnn incorporation in centrosome function, particularly in asymmetrically dividing stem cells.

Computational fluid dynamics has progressed to the point where it is now possible to simulate flows with large eddy turbulence, free surfaces and other complex features. However, the success of these models often depends on the accuracy of the advection scheme supporting them. Two such schemes are the constrained interpolation profile method (CIP) and the interpolated differential operator method (IDO). They share the same space discretisation but differ in their respectively semi-Lagrangian and Eulerian formulations. They both belong to a family of high-order, compact methods referred to as the multi-moment methods. In the absence of sufficient information in the literature, this thesis begins by taxonomising various multi-moment space discretisations and appraising their linear advective properties. In one dimension it is found that the CIP/IDO with order (2N -1) has an identical spectrum and memory cost to the Nth order discontinuous Galerkin method. Tests confirm that convergence rates are consistent with nominal orders of accuracy, suggesting that CIP/IDO is a better choice for smooth propagation problems. In two dimensions, six Cartesian multi-moment schemes of third order are compared using both spectral analysis and time-domain testing. Three of these schemes economise on the number of moments that need to be stored, with one CIP/IDO variant showing improved isotropy, another failing to maintain its nominal order of accuracy, and one of the conservative variants having eigenvalues with positive real parts: it is stable only in a semi-Lagrangian formulation. These findings should help researchers who are interested in using multi-moment schemes in their solvers but are unsure as to which are suitable. The thesis then addresses the question as to whether a multi-moment method could be implemented on a Cartesian cut cell grid. Such grids are attractive for supporting arbitrary, possibly moving boundaries with minimal grid regeneration. A pair of novel conservative fourth order schemes is proposed. The first scheme, occupying the Cartesian interior, has unprecedented low memory cost and is proven to be conditionally stable. The second, occupying the cut cells, involves a profile reconstruction that is guaranteed to be well-behaved for any shape of cell. However, analysis of the second scheme in a simple grid arrangement reveals positive real parts, so it is not stable in an Eulerian formulation. Stability in a hybrid formulation remains open to question.

This thesis is aimed at extending the spherical barotropic contour-advective semi-Lagrangian (CASL) Algorithm, written in 1996 by David Dritschel and Maarten Ambaum, to more complex test cases within the shallow-water context. This is an integral part for development of any numerical model and the accuracy obtained depends on many factors, including knowledge of the initial state of the atmosphere or ocean, the numerical methods applied, and the resolutions used. The work undertaken throughout this thesis is highly varied and produces important steps towards creating a versatile suite of programs to model all types of flow, quickly and accurately. This, as will be explained in later chapters, impacts both public safety and the world economy, since much depends on accurate medium range forecasting. There shall be an investigation of a series of tests which demonstrate certain aspects of a dynamical system and its progression into more unstable situations - including the generation and feedback of freely propagating inertia-gravity waves (hereafter “gravity waves"), which transmit throughout the system. The implications for increasing forecast accuracy will be discussed. Within this thesis two main CASL algorithms are outlined and tested, with the accuracy of the results compared with previous results. In addition, other dynamical fields (besides geopotential height and potential vorticity) are analysed in order to assess how well the models deal with gravity waves. We shall see that such waves are sensitive to the presence, or not, of sharp potential vorticity gradients, as well as to numerical parameter settings. In particular, large time-steps (convenient for semi-Lagrangian schemes) may not only seriously affect gravity waves, but may also have an adverse impact on the primary fields of height and velocity. These problems are exacerbated by a poor resolution of potential vorticity gradients, which we shall attempt to improve.

Zwei numerische Verfahren, das Upstream- und das MacCormack-Verfahren, werden im Hinblick auf ihre Eigenschaften bei der Lösung unterschiedlicher Advektionsprobleme verglichen. Das Letzere, welches eine Genauigkeit zweiter Ordnung liefert, wird in den Impulsadvektionsteil des numerischen Strömungsmodells MISKAM implementiert und anhand von Sensitivitätsstudien mit dem Upstream-Verfahren verglichen. Anschließend findet eine Modellevaluierung mit Hilfe von Datensätzen, welche am Hamburger Grenzschichtwindkanal erzeugt wurden, statt. Das Verfahren zeigt bei stabiler thermischer Modellschichtung signifikant veränderte Ergebnisse, deutlich zeigt sich die verringerte numerische Diffusion, vor allem im Bereich von Ecken und Kanten eines Hindernisses. / Two numerical schemes are compared concerning their numerical abilities when solving different advection problems. MacCormack\'s scheme which is of second order accuracy is implemented in the numerical flow model MISKAM in order to calculate the advection of momentum. It is compared to the upstream scheme with the help of sensitivity studies and with a model evaluation using wind tunnel data from the University of Hamburg. The scheme shows for stable thermical stratification significant differences near the edges of obstacles that result mainly from the reduced numerical diffusion which was the major problem when using the upstream scheme.

Questões ambientais estão no centro das discussões nas últimas décadas. A poluição atmosférica, causada pela expansão pós-revolução industrial fez surgir a necessidade de aprender a descrever, usando modelos matemáticos, esse fenômeno. Com esse conhecimento pode-se propor soluções que mitiguem a poluição e os danos colaterais causados ao ambiente. A dispersão de poluentes modelada por soluções analíticas, a partir das equações de advecção-difusão oferecem um conhecimento sobre cada componente que constrói a equação, característica inexistente em outras abordagens, como a numérica. Entretanto ela era incapaz de descrever propriedades que se referem à turbulência, as estruturas coerentes, causadas por componentes não-lineares suprimidas por construção das equações governantes do modelo. Este trabalho estudou uma forma de recuperar características associadas à turbulência através de uma componente fundamental em estruturas coerentes, a fase. Essa é incluída no modelo que passa a descrever manifestações da turbulência em processos de dispersão através de flutuações de pequena escala na concentração da solução do modelo sesquilinear, que é determinístico-estocástico. No decorrer do trabalho há um estudo através de variações de parâmetros para compreender os efeitos da fase no modelo. Ele também foi aplicado ao experimento de Copenhagen e a dois cenários reais com a intenção de compreender o modelo frente à variáveis micrometeorológicas assim como aprimorá-lo para simular a dispersão de poluentes oriundos de fontes de forma realística. / Environmental issues have been at the center of discussions in the last few decades. Atmospheric pollution, caused by post-industrial revolution, has increased the necessity to describe, using mathematical models, this phenomenon. With this knowledge is possible to propose solutions mitigating the pollution and collateral damages caused in the environment. The pollutant dispersion modeled by analytical solutions, from advection-diffusion equations, offers a knowledge about each component that constructs the equation, a characteristic that does not exist in other approaches, such as numerical. However it was unable to describe properties that refer to turbulence, coherent structures, caused by nonlinear components suppressed by constructing the model governing equations. This work studied a way to recover characteristics associated with turbulence through a fundamental component in coherent structures, the phase. This is included in the model which describes manifestations of turbulence in the dispersion process through the presence of small-scale concentration fluctuations in the sesquilinear model, which is deterministicstochastic. In the course of this work there is a study through variations of parameters to understand the phase effects in the model. It was also applied to Copenhagen experiment and to two real scenarios with the intention of understanding the model regarding micrometeorological variables as well as improving it to simulate the pollutant dispersion from sources in a realistic way.

O presente trabalho propõe um novo modelo para dispersão de poluentes na atmosfera, tal modelo foi idealizado no trabalho de dissertação da autora e continuou-se seu desenvolvimento nesta pesquisa. O modelo é baseado na solução semi-analítica da equação de advecção-difusão para emissão contínua, com resolução através do método de separação de variáveis e da transformada de Fourier. As condições de contorno são tratadas como infinitas reflexões do poluente no solo e no topo da camada limite atmosférica. Adiante, estas reflexões são utilizadas de modo parcial, na tentativa de considerar fenômenos da dispersão que não podem ser explicitados no modelo determinístico, de forma que os contornos podem ser entendidos como estocásticos, ou seja, pode-se interpretar os contornos como uma amostragem de uma distribuição. Além disso, é realizada uma otimização nos contornos parcialmente reflexivos, com o objetivo de desenvolver uma metodologia de otimização e determinar os valores ótimos para a reflexão parcial. Os resultados obtidos foram, primeiramente, comparados com os experimentos de Copenhagen e Hanford. Posteriormente, comparou-se o modelo com dados de concentração coletados em uma fábrica de celulose, a CMPC Celulose Riograndense. Simulou-se, também, a dispersão de poluentes emitidos por uma usina termelétrica no Brasil, que faz parte do programa de pesquisa e desenvolvimento tecnológico do setor de energia elétrica da Agência Nacional de Energia Elétrica (ANEEL). / The present work proposes a new model for pollutant dispersion in the atmosphere, this model was idealized in the dissertation work of the author and continued its development in this research. The model is based on the semi-analytic solution of the advectiondiffusion equation for continuous emission, with resolution through the method of separation of variables and the Fourier transform. The boundary conditions are treated as infinite reflections of the pollutant in the soil and at the top of the atmospheric boundary layer. These reflections are used in a partial way in the attempt to consider phenomena of dispersion that can not be explained in the deterministic model, so that the boundaries can be understood as stochastic, that is, one can interpret the boundaries as a sampling of a distribution. In addition, an optimization is performed in the partially reflective boundaries, with the purpose of developing an optimization methodology and determining the optimal values for the partial reflection. The results obtained were firstly compared with the experiments of Copenhagen and Hanford. Subsequently, the model was compared with concentration data collected at a cellulose production plant. The dispersion of pollutants emitted by a thermoelectric plant in Brazil was also simulated, which is part of the research and technological development program of the electric energy sector of the National Electric Energy Agency (ANEEL).

Hydraulic structures such as dykes and groynes are commonly used to help control river flows and reduce flood risk. The present research aims to develop an idealized model of the hydrodynamics in the vicinity of a large river bend, and the advection and mixing processes where groynes are located. In this study a curvilinear model of shallow water equations is applied to investigate chaotic advection of particles in a river bend similar in dimensions to a typical bend in the River Danube, Hungary. First, a curvilinear grid generator is developed based on Poisson-type elliptic partial differential equations. The grid generator is verified for benchmark tests concerning a circular domain and for distorted grids in a rectangular domain. It is found that multi-grid (MG) and conjugate gradient (CG) methods performed better computationally than successive over-relaxation (SOR) in generating the curvilinear grids. The open channel hydrodynamics are modelled using the shallow water equations (SWEs) derived by depth-averaging the continuity and Navier-Stokes momentum equations. Both Cartesian and curvilinear forms of the shallow water equations are presented. Both sets of equations are discretized spatially using finite differences and the solution marched forward in time using fourth-order Runge-Kutta scheme. The shallow water solvers are verified and validated for uniform flow in the rectangular channel, wind-induced set up in rectangular and circular basins, flow past a sidewall expansion, and Shallow flow in a rectangular channel with single groyne. A Lagrangian particle tracking model is used to predict the trajectories of tracer particles, and bilinear interpolation is used to provide a representation of the continuous flow field from discrete results. The particle tracking model is verified for trajectories in the flow field of a single free vortex and in the alternating flow field of a pair of blinking vortices. Excellent agreement is obtained with analytical solutions, previously published results in the literature. The combined shallow flow and Lagrangian particle tracking model is then used to simulate particle advection in the flow past a side-wall cavity containing a groyne and reasonable agreement is obtained with published experimental and alternative numerical data. Finally, the combined model is applied to simulate the shallow flow hydrodynamics, advection and mixing processes in the vicinity of groynes in river bend, the dimensions representative of a typical bend in the Danube River, Hungary.

Wool scouring is the first stage of wool processing, where unwanted contaminants are removed from freshly shorn wool. In most scouring machines wool is fed as a continuous mat through a series of water-filled scour and rinse bowls which are periodically drained. The purpose of this project is to mathematically model the scour bowl with the aim of improving efficiency. In this thesis four novel models of contaminant concentration within a scour bowl are developed. These are used to investigate the relationships between the operating parameters of the machine and the concentration of contamination within the scour bowl. The models use the advection-diffusion equation to simulate the settling and mixing of contamination. In the first model considered here, the scour bowl is simulated numerically using finite difference methods. Previous models of the scouring process only considered the average steady-state concentration of contamination within the entire scour bowl. This is the first wool scouring model to look at the bowl in two dimensions and to give time dependent results, hence allowing the effect of different drainage patterns to be studied. The second model looks at the important region at the top of the bowl - where the wool and water mix. The governing equations are solved analytically by averaging the concentration vertically assuming the wool layer is thin. Asymptotic analysis on this model reveals some of the fundamental behaviour of the system. The third model considers the same region by solving the governing equations through separation of variables. A fourth, fully two-dimensional, time dependent model was developed and solved using a finite element method. A model of the swelling of grease on the wool fibres is also considered since some grease can only be removed from the fibre once swollen. The swelling is modelled as a Stefan problem, a nonlinear diffusion equation with two moving boundaries, in cylindrical coordinates. Both approximate, analytical and a numerical solutions are found.